A two digit number is such that the product of its digit is 12. When 36 is added to this number, the digits interchange their places. Find the number

Let us assume that the required two digit number be as 10x + y

Now, as per given data,

xy = 12 and (10x + y) + 36 = 10y + x

on solving , (10x + y) + 36 = 10y + x

10x + y + 36 = 10y + x

10x – x + y – 10y + 36 = 0

9x – 9y + 36 = 0

x – y = 4 => y = x+4

Since , xy = 12 => x(x+4) = 12

x² + 4x – 12 = 0

x² + 6x – 2x – 12 = 0

x( x+6) -2(x+6) = 0

(x-2)(x+6) = 0 => x= 2 OR x = -6

Put x= 2 in xy = 12 we get y = 6

Hence the required digit is,

10(2) + 6 = 26